The Power of Series

After a small review on divergent series and Borel resummation I will discuss a geometric approach based on Picard-Lefschetz theory to study the interplay between perturbative and non-perturbative effects in the QM path integral.

Such approach can be used to characterize when the perturbative series gives the full answer and when the inclusion of non-trivial saddles--instantons--is mandatory. I will then show how a simple deformation of the original perturbation theory allows to recover the full non perturbative answer from the perturbative coefficients alone, without the need of including instanton corrections. I will illustrate this technique in examples which are known to contain non-perturbative effects, such as the (supersymmetric) double-well potential, the pure anharmonic oscillator, and the perturbative expansion around a false vacuum.

Collection/Series: 
Event Type: 
Seminar
Scientific Area(s): 
Speaker(s): 
Event Date: 
Tuesday, September 12, 2017 - 15:00 to 16:30
Location: 
Space Room
Room #: 
400